A090406 a(n) = PrimePi(n+3) - PrimePi(n).

2, 2, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1

Offset: 1

Author

Eric W. Weisstein, Nov 29 2003

Keywords

• nonn

Comments

a(n) <= 2, with equality if and only if n=1 or n+1 is in A001359. - Robert Israel, Aug 14 2015

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Hardy-Littlewood Conjectures

Crossrefs

Cf. A000720, A001359, A010051, A080545, A090405.

Programs

Maple

B:= [seq(numtheory:-pi(n),n=1..103)]:
B[4..-1] - B[1..-4]; # Robert Israel, Aug 14 2015

Mathematica

Last[#]-First[#]&/@Partition[PrimePi[Range[110]],4,1] (* Harvey P. Dale, Feb 24 2013 *)

Formula

a(n) = A010051(n+1) + A010051(n+2) + A010051(n+3). - Robert Israel, Aug 14 2015